4. Along its equator, Jupiter rotates once about its axis every 9 hours and 56 minutes. Its equatorial radius is 7.15 x 10¹ km. Calculate the centripetal acceleration in m/s² of a hypothetical person standing at the equator of Jupiter.
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- When Sedna was discovered in 2003, it was the most distant object known to orbit the Sun. Currently, it is moving toward the inner solar system. Its period is 10,500 years. Its perihelion distance is 75 AU. a. What is its semimajor axis in astronomical units? b. What is its aphelion distance?23. Planet Alpha has the same radius and 4 times the mass of the Earth. What is the best estimate for the magnitude of the gravitational field at the surface of planet Alpha? a. 10 m/s? b. 2.5 m/s? c. 20 m/s? d. 40 m/s? 24. The planet Theta has 3 times the gravitational field strength and 4 tirmes the mass of the Earth. How does the radius of Theta compare with the radius of Earth? a. rTheta = rEarth 2 b. rTheta = E"Earth 4 C. TTheta =-TEarth 3 d. TTheta VZrEartha. Calculate the acceleration due to gravity on the surface on the Moon if ithas a radius of 1 737 km and a mass of 7.35 x 10 22 kg. b. Would you feel lighter or heavier on the surface of the Moon? Explain. c. Calculate the weight of a 75.6 kg astronaut on the surface of Mars at the equator.See p. 273 of your textbook for Mars’ mass and equatorial radius. d. Explain how both a falling apple and the Moon are accelerating.
- 3. The gravitational acceleration at Earth's surface (ga) is about 10 m/s? and ge = GM/R2. What is g, at the surface of a planet with 2X Earth's mass and 3X Earth's radius?5. For a satellite to be in a circular orbit 780 km above the surface of the earth. A. What orbital speed must it be given? B. What is the period of the orbit (in hours)?7. Compare the gravitational force of attraction on a 1.0 kg. object when it is at the surface of the moon to the gravitational force on the same object when it is at the surface of Earth. (mass of the moon = 7.35 X 104 kg; radius of the moon m; mass of Earth = 6 X 104 kg; radius of Earth 22 %3D 6.4 X 10° m).
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- alt Z X C V b n m 1514 alt 1. Write the equation for the Force of gravity (weight) on the surface of the earth. 2. What is the value of little g in the equation above? 3. Calculate the force of gravity of a 20 kg mass on Mars. Radius of Mars ctrl 3.40 x 10 m Mass of Mars 6.43 x 1023 kg 4. Calculate the force between 2 asteroids. They are 1000 meters apart, one has a mass of 1,000,000 kg and the other has 10,000,000 kg. 5. The gravitational force between 2 masses is 100 newtons. What is the force if I double the mass of on of the objects? 6. The gravitational force between 2 masses is 100 newtons. What is the force if I double the distance between the masses? 7. T/F The mass of an object can change if I measure it on a different planet. 8. T/F My weight would be slightly less if I climbed to the top of the highest mountain. 9. Draw a free body diagram (force diagram) of an object suspended from a string. 10. Calculate the tension force on string A in the diagram below. Assume a…1. The mass of the moon is 7.34767309 x 1022kg. The moon has a radius of 1,737.1 km. Given the Universal Gravitational constant of G = 6.67 x 10-11 Nm²/kg². a. Calculate the acceleration due to gravity of the moon. b. The mass of a space shuttle is 2.18 x 106 kg and orbits the moon at 175 km. What is the Force between the moon and the space shuttle?4. Compute the differential tidal force AF exerted on the Earth by Mars when it's at opposition. Express your result as a numerical fraction of the differential tidal force exerted by the Moon, 2GMMoonm RO where ro = 384,000km = 0.00257AU is the Earth-Moon distance and MMoon = 7.2 x 1022kg is the mass of the Moon. Repeat to find the differential tidal force AF exerted by Jupiter at opposition, also expressed as a fraction of AEMaen. (Assume that the Moon, Earth, Mars, and Jupiter are on circular coplanar orbits.)